The probability that any particular component of a certain type works in a satisfactory manner is p. If n of these components are independently selected, then the statistic X, the number among the...

The probability that any particular component of a certain type works in a satisfactory manner is p. If n of these components are independently selected, then the statistic X, the number among the selected components that perform in a satisfactory manner, is sufficient for p. You must purchase two of these components for a particular system. Obtain an unbiased statistic for the probability that exactly one of your purchased components will perform in a satisfactory manner. [Hint: Start with the statistic U, the indicator function of the event that exactly one of the first two components in the sample of size n performs as desired, and improve on it by conditioning on the sufficient statistic.]